UPSC Prelims 2021 · CSAT

Question 77: Basic Numeracy

X said to Y, “At the time of your birth I was twice as old as you are at present.” If the present age of X is 42 years, then consider the following statements :

1.8 years ago, the age of X was five times the age of Y.
2.After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct ?

a1 only

b2 only

cBoth 1 and 2

dNeither 1 nor 2

AnswerUPSC’s answer is (b).

Let Y's present age be y. At Y's birth, X was 42 − y years old, which equals twice y, so 42 − y = 2y and y = 14. Statement 1: 8 years ago X was 34 and Y was 6; 5 × 6 = 30, not 34. False. Statement 2: after 14 years X is 56 and Y is 28; 56 = 2 × 28. True. Only 2 is correct. Remember: 'at the time of your birth' means X's age then is X's present age minus Y's age.

1. 8 years ago X was 34 and Y was 6; five times 6 is 30, not 34.
2. After 14 years X is 56 and Y is 28, and 56 = 2 × 28.

How you could have got this

If you were sure statement 1 is not correct, (a) and (c) go: each of them includes 1.
What you needed to know: 8 years ago X was 34 and Y was 6; five times 6 is 30, not 34.
Then, if you were sure statement 2 is correct, (d) goes: it leaves 2 out.
What you needed to know: After 14 years X is 56 and Y is 28, and 56 = 2 × 28.

Only (b) is left. This one needs every statement.

Which options go is worked out from UPSC’s key and the options, not by a model.

Why each option is right or wrong

(a) Statement 1 is false: 8 years ago X was 34 and Y was 6, and 5 × 6 = 30.
(b) Right: Y is 14, and in 14 years X is 56, twice Y's 28.
(c) Statement 1 is false, so both cannot be correct.
(d) Statement 2 holds, so this fails.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.